Abstract
The present study aims to investigate the effect of a nonlinearly stretchable rate and inconstant heat generation (sink) on heat transfer in a Carreau fluid flowing via a stretchable cylinder. The impact of temperature-dependent thermal conductance and thermal radiation is considered. Suitable similarity variables are applied to transform complex partial differential equations (PDEs) into ordinary differential equations (ODEs). The determined series solutions of the highly nonlinear ODEs utilizing the homotopy analysis methodology are validated with earlier published results for certain limited cases. Diagrams and tables are outlined to scrutinize the effects of the inconstant heat generating (sink) on the liquid motion and heat transference for a linear and nonlinear stretching rate. The analysis reveals that disturbance happens in the temperature outline in the liquid domain with heat generation and nonlinearly stretchable rate. The nonlinearly stretched position has enhanced the rapidity and temperature outline in all constraints excluding the temperature in an interior heat bowl condition. Moreover, the temperature profile in the heat source/sink situation has an opposite characteristic in dilatant liquid, n>1,$n > 1,$ and pseudo-plasticity liquid, n<1$n < 1$ for increasing values of the Weissenberg number. The discussions are relevant to manufacturing wire coating, plastic covers, paper production, and the whirling of fiber.